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Re: Re: Radicals simplify

  • To: mathgroup at
  • Subject: [mg106409] Re: [mg106378] Re: [mg106361] Radicals simplify
  • From: "David Park" <djmpark at>
  • Date: Mon, 11 Jan 2010 18:53:52 -0500 (EST)
  • References: <> <31173649.1263207631979.JavaMail.root@n11>

This can be simplified to the posters desired expression with Presentations.


MapAt[FactorOut[x^2, Identity, CreateSubexpression], %, 1]  
Simplify[%, x >= 0] // ReleaseSubexpressions[]  

(x^6 y^3)^(1/4)
(x^4 y^3 (x^2))^(1/4)
x (x^2 y^3)^(1/4)

We factored x^2 out of the product and protected it by making it a
Subexpression. Then used Simplify and released the Subexpression.

David Park
djmpark at  

From: Andrzej Kozlowski [mailto:akoz at] 

On 10 Jan 2010, at 17:30, francix wrote:

> Hi,
> I am using Matematica 7 and need some help with Radicals.
> If I do
> Simplify[(x^4 y^3)^(1/4), x >= 0] I correctly have
> x (y^3)^(1/4)
> But If I do
> Simplify[(x^6 y^3)^(1/4), x >= 0] I get
> (x^6 y^3)^(1/4) and not the correct answer  x(x^2 y^3)^(1/4)
> Thanks in advanced.

The problem is that your desired formula has a higher ComplexityFunction 
than the one returned by Mathematica. Mathematica's default 
ComplexityFunction is close to LeafCount and






The quickest way to get the answer close to the one you want in this 
case is:

Refine[(x^6*y^3)^(1/4), x >= 0]


To get exactly the answer you want you will need to play with 
ComplexityFunction, which in this case will be tricky.

Andrzej Kozlowski

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